Depends on the lens. Some lenses can go beyond infinity focus (I've even heard of some that can go beyond in AF but don't in manual!), which would allow the AF system to do just fine in focusing at infinity in the standard way, since it could bracket either side as normal.
Other camera systems might detect the particular lens and use the aperture information, etc. to simply focus a little bit beyond a pre-calculated hyperfocal distance, if it has been hunting near there and not getting anything..
Anyway, regardless of the solution, all of my autofocus lenses do just fine at infinity, somehow or another as long as I don't treat my camera like some godly omniscient entity. I intentionally point it at something in infinity that has a nice clean contrasty edge to help it out (that goes for ANY focal distance if you want the fastest and most accurate AF), and never run into any problems.
So if you're doing that, and it's still failing, then that's probably a broken lens. Whether you get it repaired depends on warranty, whether it's worth going without it for 2 weeks, how often you focus at infinity at 60-70mm, etc. Hard for us to say.